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Ambiguity resolution with PPP aims at effectively reducing the long convergence time. The research in this dissertation explores its potential for both dual-frequency signals and triple-frequency signals. One of the most popular PPP ambiguity resolution strategies with dual-frequency GNSS signals is to first fix the L1/L2 wide-lane ambiguities in the geometry-free approach and then fix the L1 ambiguities in the geometry-based approach. A software package has been developed to evaluate the PPP ambiguity resolution performance with this strategy, including position accuracy, time-to-first-fix and fixing availability of both L1/L2 wide-lane ambiguity and L1 ambiguity, etc. A new model has been developed to improve the performance of PPP ambiguity resolution with dual-frequency signals, in which the L1 fractional bias is split into one direction-independent and three directional-dependent components for each satellite. Better performance can be obtained at both server and client rover side using the new model, but the L1 ambiguity fixing time still requires around 30 minutes on average. A new method of instantaneous PPP ambiguity resolution with triple-frequency signals has been proposed, which involves first fixing the L2/L5 wide-lane ambiguities in geometry-free approach and then fixing the L1/L2 wide-lane ambiguities in geometry-based approach. Based on the test results with extensive MATLAB simulation datasets and newly available BeiDou real signal datasets, both L2/L5 wide-lane ambiguity and L1/L2 wide-lane ambiguity can be fixed instantaneously and reliably using a single epoch of triple-frequency measurements. A carrier smooth carrier technique has been proposed to reduce the measurement noise for PPP ambiguity resolution with triple-frequency signals. PPP can achieve horizontal positioning accuracy better than 5 cm and 3D positioning accuracy better than 10 cm, with the convergence time less than two minutes. This performance is comparable to RTK.